Bielsa, who also steered Bilbao to the Copa del Rey final in his first season in charge of the north-coast club, saw Radamel Falcao net a stunning double to help Atleti to a 3-0 win in Bucharest.
Athletic, playing in only their second European final and first for 35 years, tried to replicate the same attacking intensity that brought exciting knockout stage wins over Manchester United and Schalke.
But for the first 70 minutes the Bilbao club, who only field players of Basque origin, had their cutting edge blunted by an Atletico side moulded in the steely ways of former midfield enforcer Diego Simeone.
"We did not defend well, we were not decisive in attack, we played much less than we are capable of doing," Bielsa said.
"The difference between the two teams is now what we saw today and the finger of responsibility points directly to the person who is in charge."